A101800
a(n)= abs(det[A000166(i+j+1)]), i,j=0...n, is the absolute value of the Hankel determinant of order n+1 of the derangements numbers, cf. A000166.
Original entry on oeis.org
0, 1, 16, 2160, 4644864, 220962816000, 126311423016960000, 97655159393202733056000000, 2873961139404949958783139840000000000, 5118723340142578530942677236206891171840000000000
Offset: 0
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a[n_] := Table[Subfactorial[i+j+1], {i, 0, n}, {j, 0, n}] // Det // Abs;
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Aug 18 2024 *)
A227143
Hankel determinants of order n of A225439(n): a(n)=det[A225439(i+j-2)], i,j=0..n, n>=0.
Original entry on oeis.org
1, 1, 12, 567, 122472, 126660105, 640190834712, 15987980408180508, 1985745116187976972608, 1231754497376142871049675940, 3826847477714307687323719819461000, 59670909707615018862830973519922857945375
Offset: 0
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with(LinearAlgebra):
A225439 := proc(n) add(binomial(k,n-k)*3^(k)*(-1)^(n-k)*binomial(n+k-1,n-1), k=0..n) end:
hank0:= (i, j)-> A225439(i+j-2):
a:= proc(n) Determinant(Matrix(n,n,hank0)) end:
seq(a(n), n=0..10);
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A225439[n_] := Sum[Binomial[k, n-k]*3^k*(-1)^(n-k)*Binomial[n+k-1, n-1], {k, 0, n}]; a[n_] := Det[Table[A225439[i+j-2], {i, n}, {j, n}]]; a[0] = 1; Table[ a[n], {n, 0, 11}] (* Jean-François Alcover, Nov 07 2016 *)
A227379
Hankel determinants of order n of A225439(n): a(n) = det[A225439(i+j-1)], i,j=0..n, n>=0.
Original entry on oeis.org
1, 3, 45, 3402, 1299078, 2507870079, 24487299427734, 1209640056157393380, 302358334494179897593596, 382459771435292361460924379370, 2448391839613471201062299337071282925
Offset: 0
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with(LinearAlgebra):
A225439 := proc(n) add(binomial(k, n-k)*3^(k)*(-1)^(n-k)*binomial(n+k-1, n-1), k=0..n) end:
hank1:= (i, j)-> A225439(i+j-1):
a:= proc(n) Determinant(Matrix(n, n, hank1)) end:
seq(a(n), n=0..10);
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A225439[n_] := Sum[Binomial[k, n-k]*3^k*(-1)^(n-k)*Binomial[n+k-1, n-1], {k, 0, n}]; a[n_] := Det[Table[A225439[i+j-1], {i, n}, {j, n}]]; a[0] = 1; Table[ a[n], {n, 0, 11}] (* Vaclav Kotesovec, Feb 24 2019, after Jean-François Alcover *)
Showing 1-3 of 3 results.
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